TY - JOUR ID - 55701 TI - An Adaptive Physics-Based Method for the Solution of One-Dimensional Wave Motion Problems JO - Civil Engineering Infrastructures Journal JA - CEIJ LA - en SN - 2322-2093 AU - Shafiei, Masoud AU - Khaji, Naser AD - Ph.D., Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran AD - Professor, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran. Y1 - 2015 PY - 2015 VL - 48 IS - 2 SP - 217 EP - 234 KW - Adaptive solution KW - Deslauries-Dubuc wavelets KW - Multi-resolution analysis KW - Physics-based solution KW - Smoothing splines DO - 10.7508/ceij.2015.02.001 N2 - In this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). The solution of the problem includes two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, adaptive points are determined using the wavelet theory. This part is done employing the Deslauries-Dubuc (D-D) wavelets. By solving the problem in the first step, the domain of the problem is discretized by the same cells taking into consideration the load and characteristics of the structure. After the first trial solution, the D-D interpolation shows the lack and redundancy of points in the domain. These points will be added or eliminated for the next solution. This process may be repeated for obtaining an adaptive mesh for each step. Also, the smoothing spline fit is used to eliminate the noisy portion of the solution. Finally, the results of the proposed method are compared with the results available in the literature. The comparison shows excellent agreement between the obtained results and those already reported. UR - https://ceij.ut.ac.ir/article_55701.html L1 - https://ceij.ut.ac.ir/article_55701_cf5352fd485860246fc57697a5b98f1f.pdf ER -